In a pumping system, the controlled quantity and the reference for the control affect the operation of the pumping system while also providing identifying factors for the process.
Based on the typical control quantities of a pump system; flow rate and pressure, the pumping systems can be classified into four general types: (Ahonen et al., 2011b)
– Constant-flow constant-pressure systems – Variable-flow variable-pressure systems – Constant-flow variable-pressure systems – Variable-flow constant-pressure systems
With these quantities, it is possible to determine how the pump is driven and also derive additional quantities of the pump, such as the fluid level of a reservoir. The typical reser-voirs fluid level changes over time, which requires the pump to be driven with a certain operation pattern. This provides identifying characteristics of the pumping process. The tasks the pump system is used to fulfill can require sequential or constant pump operation.
Pumping tasks can be divided into process function classes: (Ahonen et al., 2011b)
– On/off-controlled repeated pumping task – Controlled pumping in an open loop system
– Pressure-controlled pumping in an open loop network
– Process/volume flow-controlled pumping in a closed loop network
On/off repeated pumping task is the simplest process function class. An example of this process function class is the emptying and filling of a reservoirs fluid level. In this class, there is typically a height difference between the reservoirs fluid levels and system is open-looped. This pumping task can be variable pressure variable flow or variable pres-sure constant flow (Ahonen et al., 2011b).
Controlled pumping in an open loop system is a class in which the fluid is continuously transferred between locations. As an example for this class, is a continuous pumping to maintain a constant fluid level between to reservoirs. As the name suggests, this class has an open loop and can be controlled for example by fluid output pressure, flow rate or fluid level. The tasks in this class can vary depending on the required fluid elevation or pressure boost (Ahonen et al., 2011b).
Pressure controlled pumping in an open loop network is a class in which the pumps task is to provide certain constant pressure regardless of the flow rate of the fluid. A typical example of this is the water system in which the households, offices and industry are con-nected to. The control is achieved via fluid pressure and is usually continuous (Ahonen et al., 2011b).
Process/volume flow-controlled pumping in a closed loop network is a process class which is closed loop and the flow rate or a derivative of the variable is controlled. An example of this class is the heat exchanger. This class can be on/off, sequential or contin-uous. Because of the closed loop, the system curve of the process is dynamic loss heavy and the use of speed control can be effective (Ahonen et al., 2011b).
3 Data processing and machine learning
Data measurements can provide a lot of information alone and can even be combined for further information. However, in measurements there can occur errors, either from the environment or a possible statistical anomaly. These include the accuracy of the used equipment, repeatability of the measurements, uncertainty of the readings, the confidence level of the measurement (Baker, 2000). The measurement can even be erroneous because of the range of the used instrumentation. Also, the possibility of measurement drifting and calibration can affect the measurement. These can affect the estimations of the property being measured.
The measurement data can be filtered in order to provide useful information and to remove noise from the original signal. For this purpose, digital filters are applied. Then the data can be used for creating and training machine learning algorithms. In this chapter, first the concept of digital filters is discussed and then several machine learning algorithms are introduced.
3.1 Digital filters
In order to make digital signals one needs to take continuous analog signals and sample them at a discrete rate in order to recreate the original in a digital form signal. This is referred to as analog-to-digital conversion (ADC) (Schlichth¨arle, 2011). Digital filtering is a form of signal processing, where unwanted components or features are removed from the original digital signal (Thyagarajan, 2019). Digital filters applications include digital communications such as transmitting information via digital signals, digital image pro-cessing and propro-cessing and transmitting of audio signals, such as speech.
There are several different types of digital filters such as filters that remove components either over or under a given frequency threshold i.e. cutoff frequency. Digital filters can also be categorized by their impulse responses and structure (Schlichth¨arle, 2011). The digital filter design is important, because as the filter alters the original signal, the re-sult can be a distorted signal if the filter is designed incorrectly. The signal can become distorted due to under- or oversampling, quantization error, channel reactance causing a signal overlap or even timing errors (Thyagarajan, 2019).
The importance of filter design is highlighted when considering two poor filter design practices, which are the lack of understanding either the filter parameters and their effects or the lack of understanding the consequences of digital filtering (Widmann et al., 2015).
Everything from the filter type, filter response to the cutoff frequency should be designed so that it produces the desired effect on the signal and avoids unwanted distortions. To recognize filter distortions and design flaws, a couple of methods are suitable. For ex-ample, the use of test signal on the filters to observe the behaviour of the parameters and properties. Also, inspecting the components that are filtered out can give useful informa-tion on the filters performance.
In order to capture a digital signal it needs to be sampled at twice the rate in order to cap-ture the original signal (Dieter et al., 2005). This is also known as the nyquist frequency.
Because of this frequency dependency, it can require a lot of power consumption. By reducing or changing the sampling rate, the power consumption can be reduced. Varying the sampling time can also be a way to optimize available the processing power (Schinkel et al., 2002). Varying sampling rate can in some instances provide more accurate infor-mation with more efficiency than a static sampling rate. In situations where the measure-ment conditions can have sharp and dynamic changes, being able to change the sampling rate accordingly can improve the the accuracy of the measurements (Korprasertsak and Leephakpreeda, 2018). This would allow the high sampling rate during high frequency changes so that the effect called aliasing can be prevented. Aliasing occurs when the sam-pling rate is below nyquist frequency. Combining the varying samsam-pling time along with measurement errors and instrumentation inaccuracies there can occur time variations that cause control processes to be out of sync and possibly use sample data with different time stamps, which is especially important in communication applications (Pazos et al., 2019).
Asynchronous operation between all applications is not time sensitive, but in cases of network control systems (NCS) the varying sample times and delays in timing can lead to instability. This can be the case when a high sampling rate can take up too much of the networks available bandwidth and preventing access. In Osella et al. (2016) it was proposed that the network has a centralized controller which operates synchronously and determines the sampling rate at each sampling instant while also handling the computing.
Next, two filters, median filter and kalman filter, are introduced and their applications are discussed.
Median filter
The median filter is widely used in statistics, but has gained applications in digital im-age processing and analysis, which partially be credited to its computational simplicity and performance abilities, such as speed (Meguro and Taguchi, 2000; Pitas and Veneet-sanopoulos, 1990). Median filter is considered a nonlinear filter, which handle signal-dependent noise and non-Gaussian statistics in signals more efficiently than linear filters (Solovyeva, 2016). The median filter, as the name suggests uses the median formula in the filtering process. The median is calculated as (Pitas and Veneetsanopoulos, 1990):
med(xi) = where thexis the ith order statistic, v is the observation window size to one direction of the sample andm is the number of observations. By taking the median of each of the data samples using a2v + 1 window, we get a one dimensional median filter which is expressed as follows (Pitas and Veneetsanopoulos, 1990):
yi =med(xi-v, .., xi, .., xi+v) i∈Z, (3.2) where theyi is the output of the filter sequence. This filter is also known as a moving median.
Kalman filter
Kalman filter is is a popular algorithm in information processing named after Rudolf E. K´alm´an (Faragher, 2012). This common data fusion algorithm if favored due to its small computational requirements, good recursive properties and the ability for optimal estimation of one-dimensional linear systems using Gaussian error statistics. Along with smoothing noisy data, kalman filter is suitable for parameter estimation. The kalman filter can be expressed with the following equation:
ˆ
xt|t =xˆt|t-1+Kt(zt−Htxˆt|t-1), (3.3)
where thexˆt|tis a state vector containing the pumps variable data such as rotational speed at timet,zt is the vector of measurements at timet, Ht is the transformation matrix that maps the pump variables into measurement domain andKt is the kalman filter gain. A special case of kalman filter, which functions as a digital low pass filter, can be applied as a one dimensional filter can be obtained by adjusting Eq. 3.3 (Dyason et al., 2017):
xt =xx-1+K(zt−xt-1), (3.4) wherextis the output at timet,ztis the measurement at timetandKis the kalman gain.
The gain can be calculated with:
K = ∆t
τ , (3.5)
where∆tis the time step between samples andτ the kalman gain constant. The time step between samples is calculated with∆t=tn−tn-1.